First of all, pick out a good multi-vitamin, then you can add from there. On top of that I would pick up a bottle of vitamin C; some research has shown that megadoses of vitamin C help to prevent certain illnesses, such as the common cold. Vitamin C plays an important role in the production of white blood cells and the production of interferon, which is an antibody that coats the WBCs. Most vitamin C supplements come in the form of 500mg, which coupled with your multi-vitamin, and diet sources, should be more than enough vitamin C. I wouldn't worry too much about overdose, because vitamin C has a low toxicity level, and the amount you would have to take to overdose is enormous. It's the fat soluble vitamins (A,D,E,K) you really have to worry about overdosing. Most excess water soluble vitamins (including vitamin C) are just urinated out when in excess.
Vitamin E also plays an important role in a healthy immune system. It plays a role in producing certain cells that aid to destroy invading bacteria. The amount you get in your multi-vitamin along with dietary sources should be enough.
Omega-3 fatty acids, such as those found in fish oils, can help boost the immunity. Omega-3s work with vitamin E to help boost the immune system in a number of ways. I take a lot of fish oil.
Also, if you're not already supplementing with L-glutamine, then pick up some of that too. It's the most abundant amino acid found in muscle tissue, and is a primary fuel for the immune system.
There are other vitamins and minerals that help boost the immune system, such as zinc, vitamin D, and selenium, but if you're taking a good multi-vitamin, you should have those covered.
So here's a checklist of vitamins you can supplement in addition to a good multi-vitamin:
1.) Vitamin C (500mg ED)
2.) L-Glutamine
3.) Omega-3 (Fish Oil)
Also, Garlic is also something people supplement with to help boost the immune system, for whatever reason (I've never looked it up). Probably boosts the production of certain cells or antibodies, like a lot of things do. You can supplement it and/or you can add it to your dietary intake via food sources (by adding garlic to your foods).
I think with a balanced, healthy diet, along with proper supplementation, you can do a lot to fend off sickness. I rarely get sick; maybe once a year I'll get a cold, but to me it's just a runny nose for a few days. Eat healthy, be healthy!